A hemispherical body of radius R is placed in a uniform electric field E. What is the flux linked with the curved surface if, the field is (a) parallel to the base, (b) perpendicular to the base.

Explanation

Considering the hemispherical body as a closed body with a curved surface (CS) and a plane surface (PS), the total flux `(phi)` linked with the body will be zero, as no charge is enclosed by the body
I,e., `phi = phi_(CS) + phi_(PS) = 0` .. (i)
It implies that number of electric field lines leaving the surface.
(a) When field is parallel to the base,
`phi_(PS) = E xx pi R^(2) cos 90^(@) = 0`
`:.` From (i), `phi = phi_(CS) = 0`
(b) When field is perpendicular ot the base,
`phi_(PS) = E xx pi R^(2) cos 180^(@) = -E pi R^(2)`
`:.` from (i) `phi_(CS) - E pi R^(2) = 0` or `phi_(CS) = E pi R^(2)`